Today’s agenda:

Measuring Instruments: ammeter, voltmeter, ohmmeter.You must be able to calculate currents and voltages in circuits that contain “real” measuring instruments.

RC Circuits.You must be able to calculate currents and voltages in circuits containing both a resistor and a capacitor. You must be able to calculate the time constant of an RC circuit, or use the time constant in other calculations.

You know how to calculate the current in this circuit:

Measuring Instruments: Ammeter

V

R

.V

I = R

If you don’t know V or R, you can measure I with an ammeter.

.V

I = R+r

To minimize error the ammeter resistance r should very small.

Any ammeter has a resistance r.Any ammeter has a resistance r. The current you measure is

r

Example: an ammeter of resistance 10 m is used to measure the current through a 10 resistor in series with a 3 V battery that has an internal resistance of 0.5 . What is the percent error caused by the nonzero resistance of the ammeter?

V=3 V

R=10

r=0.5

Actual current:

VI =

R+r

3I =

10+0.5

I = 0.286 A = 286 mA

You might see the symbol used instead of V.

V=3 V

R=10

r=0.5

Current with ammeter:

A

VI =

R+r+R

3I =

10+0.5+0.01

I = 0.285 A = 285 mA RA

0.286-0.285

% Error = 1000.286

% Error = 0.3 % Not bad in a Physics 2135 lab!

A Galvanometer

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/galvan.html#c1

When a current is passed through a coil connected to a needle, the coil experiences a torque and deflects. See the link below for more details.

An ammeter (and a voltmeter—coming soon) is based on a galvanometer. OK, everything is electronic these days, but the principles here still apply.

We’ll learn about galvanometers later.

For now, all you need to know is that the deflection of the galvanometer needle is proportional to the current in the coil (red).

A typical galvanometer has a resistance of a few tens of ohms.

Hold it right there. Didn’t you say an ammeter must have a very small resistance. Is there a physics mistake in there somewhere?

A galvanometer-based ammeter uses a galvanometer and a shunt, connected in parallel:

A

I

GRG

RSHUNT

IG

ISHUNT

I

Everything inside the blue box is the ammeter.

The resistance of the ammeter is

A G SHUNT

1 1 1R R R

G SHUNTA

G SHUNT

R RR

R R

Homework hint: “the galvanometer reads 1A full scale” means a current of IG=1A produces a full-scale deflection of the galvanometer needle. The needle deflection is proportional to the current IG.

If you want the ammeter shown to read 5A full scale, then the selected RSHUNT must result in IG=1A when I=5A. In that case, what are ISHUNT and VAB (=VSHUNT)?

GRG

RSHUNT

IG

ISHUNT

I

Homework hint: “the galvanometer reads 1A full scale” means a current of IG=1A produces a full-scale deflection of the galvanometer needle. The needle deflection is proportional to the current IG.

If you want the ammeter shown to read 5A full scale, then the selected RSHUNT must result in IG=1A when I=5A. In that case, what are ISHUNT and VAB (=VSHUNT)?

A B

Homework hint: “the galvanometer reads 1A full scale” means a current of IG=1A produces a full-scale deflection of the galvanometer needle. The needle deflection is proportional to the current IG.

If you want the ammeter shown to read 5A full scale, then the selected RSHUNT must result in IG=1A when I=5A. In that case, what are ISHUNT and VAB (=VSHUNT)?

A galvanometer-based ammeter uses a galvanometer and a shunt, connected in parallel:

GRG

RS

IG

IS

I

A G S

1 1 1R R R

Example: what shunt resistance is required for an ammeter to have a resistance of 10 m, if the galvanometer resistance is 60 ?

S A G

1 1 1R R R

G A

SG A

60 .01R RR 0.010

R -R 60-.01

The shunt resistance is chosen so that IG does not exceed the maximum current for the galvanometer and so that the effective resistance of the ammeter is very small.

(actually 0.010002 )

To achieve such a small resistance, the shunt is probably a large-diameter wire or solid piece of metal.

G A

SG A

60 .01R RR 0.010

R -R 60-.01

Web links: ammeter design, ammeter impact on circuit, clamp-on ammeter (based on principles we will soon be studying).